Quantum Geometric Bounds in Non-Hermitian Systems

• URL: http://arxiv.org/abs/2512.23708v1
• Date: Mon, 29 Dec 2025 18:59:41 GMT
• Title: Quantum Geometric Bounds in Non-Hermitian Systems
• Authors: Milosz Matraszek, Wojciech J. Jankowski, Jan Behrends,
• Abstract summary: We find unique bounds on non-Hermitian quantum geometric tensors, generalized two-point response correlators, conductivity tensors, and optical weights.<n>We demonstrate that the non-Hermitian geometric constraints on response functions naturally arise in open quantum systems governed by out-of-equilibrium Lindbladian dynamics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We identify quantum geometric bounds for observables in non-Hermitian systems. We find unique bounds on non-Hermitian quantum geometric tensors, generalized two-point response correlators, conductivity tensors, and optical weights. We showcase these findings in topological systems with non-Hermitian Chern numbers. We demonstrate that the non-Hermitian geometric constraints on response functions naturally arise in open quantum systems governed by out-of-equilibrium Lindbladian dynamics. Our findings are relevant to experimental observables and responses under the realistic setups that fall beyond the idealized closed-system descriptions.

Related papers

• Quantum geometrical effects in non-Hermitian systems [0.0]
  We show that the behavior of a non-Hermitian system is best understood in terms of quantum geometry.<n>We show that the non-Hermitian quantum metric appears in the response of the system upon time-periodic modulation.
  arXiv  Detail & Related papers  (2025-12-08T08:03:41Z)
• Nonequilibrium Probes of Quantum Geometry in Gapless Systems [0.0]
  Much of our understanding of gapless many-body quantum systems stems from their low-energy descriptions as conformal field theories.<n>This is especially true in 1+1 dimensions, where such theories have an infinite-dimensional parameter space induced by their conformal symmetry.<n>We reveal the associated quantum geometry by considering finite systems driven by time-dependent conformal transformations.
  arXiv  Detail & Related papers  (2025-11-12T19:00:05Z)
• Non-Hermitian quantum geometric tensor and nonlinear electrical response [18.598621685803767]
  We show that the non-Hermitian quantum geometric tensor governs electrical responses in systems with a spectral line gap.<n>We establish a universal link between nonlinear dynamics and the QGT, thereby connecting quantum state geometry to observable transport phenomena.<n>This framework unifies non-Hermitian response theory by revealing how geometric degrees of freedom encode transport in open and synthetic quantum matter.
  arXiv  Detail & Related papers  (2025-09-15T10:36:08Z)
• Grassmann Variational Monte Carlo with neural wave functions [45.935798913942904]
  We formalize the framework introduced by Pfau et al.citepfau2024accurate in terms of Grassmann geometry of the Hilbert space.<n>We validate our approach on the Heisenberg quantum spin model on the square lattice, achieving highly accurate energies and physical observables for a large number of excited states.
  arXiv  Detail & Related papers  (2025-07-14T13:53:13Z)
• Work Statistics and Quantum Trajectories: No-Click Limit and non-Hermitian Hamiltonians [50.24983453990065]
  We present a framework for quantum work statistics in continuously monitored quantum systems.<n>Our approach naturally incorporates non-Hermitian dynamics arising from quantum jump processes.<n>We illustrate our theoretical framework by analyzing a one-dimensional transverse-field Ising model under local spin monitoring.
  arXiv  Detail & Related papers  (2025-04-15T23:21:58Z)
• Quantum geometric bounds in spinful systems with trivial band topology [0.0]
  We derive quantum geometric bounds in spinful systems characterized by a single $mathbbZ$ index protected by a spin gap.<n>Our bounds provide geometric conditions on the spin topology, distinct from the known quantum geometric bounds associated with Wilson loops and nontrivial band topologies.<n>We benchmark these findings with first-principles calculations in elemental bismuth realizing a nontrivial even spin-Chern number.
  arXiv  Detail & Related papers  (2025-01-27T19:00:02Z)
• Quantum entanglement and non-Hermiticity in free-fermion systems [7.537786338273108]
  This review article reports rapid progress on the generalization and application of entanglement in non-Hermitian free-fermion quantum systems. In particular, we focus on how entanglement concepts are extended to non-Hermitian systems from their Hermitian free-fermion counterparts. We highlight various concrete studies, demonstrating that entanglement entropy remains a powerful diagnostic tool for characterizing non-Hermitian physics.
  arXiv  Detail & Related papers  (2024-08-21T14:25:14Z)
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [43.80709028066351]
  Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system.<n>This paper explores how a finite density of local measurement modifies a given state's entanglement structure.
  arXiv  Detail & Related papers  (2023-10-04T09:51:00Z)
• Nontrivial worldline winding in non-Hermitian quantum systems [3.8601741392210434]
  We investigate non-Hermitian physics in interacting quantum systems, e.g., various non-Hermitian quantum spin chains. We study the direct physical implications of such nontrivial worldline winding, which bring additional, potentially quasi-long-range contributions to the entanglement entropy.
  arXiv  Detail & Related papers  (2023-07-03T18:00:02Z)
• High-dimensional monitoring and the emergence of realism via multiple observers [41.94295877935867]
  Correlation is the basic mechanism of every measurement model.<n>We introduce a model that interpolates between weak and strong non-selective measurements for qudits.
  arXiv  Detail & Related papers  (2023-05-13T13:42:19Z)
• Geometric phases along quantum trajectories [58.720142291102135]
  We study the distribution function of geometric phases in monitored quantum systems. For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle. For the same parameters, the density matrix does not show any interference.
  arXiv  Detail & Related papers  (2023-01-10T22:05:18Z)
• Bridging the gap between topological non-Hermitian physics and open quantum systems [62.997667081978825]
  We show how to detect a transition between different topological phases by measuring the response to local perturbations. Our formalism is exemplified in a 1D Hatano-Nelson model, highlighting the difference between the bosonic and fermionic cases.
  arXiv  Detail & Related papers  (2021-09-22T18:00:17Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• Quantum Non-equilibrium Many-Body Spin-Photon Systems [91.3755431537592]
  dissertation concerns the quantum dynamics of strongly-correlated quantum systems in out-of-equilibrium states. Our main results can be summarized in three parts: Signature of Critical Dynamics, Driven Dicke Model as a Test-bed of Ultra-Strong Coupling, and Beyond the Kibble-Zurek Mechanism.
  arXiv  Detail & Related papers  (2020-07-23T19:05:56Z)
• Probing chiral edge dynamics and bulk topology of a synthetic Hall system [52.77024349608834]
  Quantum Hall systems are characterized by the quantization of the Hall conductance -- a bulk property rooted in the topological structure of the underlying quantum states. Here, we realize a quantum Hall system using ultracold dysprosium atoms, in a two-dimensional geometry formed by one spatial dimension. We demonstrate that the large number of magnetic sublevels leads to distinct bulk and edge behaviors.
  arXiv  Detail & Related papers  (2020-01-06T16:59:08Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.